Widget, is a reusable component of UI that is present on multiple pages. Since the widget is present on multiple pages, it should not be documented in the documentation of any one of those pages, but instead there should be a dedicated document for documenting the widget.
Note that this is not the laundry list of all atom level UI components. The kitchen sink UI components, style guide etc are documented as part of “Development Manual” and not “Product Manual”. A widget is a widget only if end users are actively aware of it, like the Mail Compose widget of Gmail, or popup search or login dialog of some sites, users are aware they are intersecting with “Search dialog” and not the “Blog Index Page” for example, as search dialog is present on many pages, not just blog index page. Similarly if the search dialog is made up of “Primary Button” or whatever, the user is not really thinking that yes this type of UI element is present on many pages. Primary button and all its states etc goes in the developer manual.
The documentation of a Widget mirrors the documentation of a page, just that widget does not have a URL. Widget may have parameters, so the Parameters heading can be still included.